ASTR 160: Frontiers and Controversies in Astrophysics

Lecture 6

 - Microlensing, Astrometry and Other Methods


The class begins with a discussion on transits – important astronomical events that help astronomers to find new planets. The event occurs when a celestial body moves across the face of the star it revolves around and blocks some of its light. By calculating the amount of light that is being obscured astronomers can obtain important information about both star and planet, such as size, density, radial velocity and more. The concept of planetary migration is explained in order to better understand the dramatic differences between bodies in the Inner and Outer Solar System. Finally, potential problems in the Solar System that may occur as a result of migration are addressed.

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Frontiers and Controversies in Astrophysics

ASTR 160 - Lecture 6 - Microlensing, Astrometry and Other Methods

Chapter 1. Complexities and New Observations on Hot Jupiters [00:00:00]

Professor Charles Bailyn: You’ll recall that where we got to last time is that there are lots of Hot Jupiters; lots of Hot Jupiters. And the alternative theories that were presented to explain the evidence for Hot Jupiters–the evidence for Hot Jupiters comes in this form of these velocity curves, where you plot the radial velocity versus time of the star. And the star goes back and forth, and you infer from that that there must be a planet going around it, which is pulling the star back and forth. And some alternative explanations were proposed to explain these kinds of data. Those alternative explanations didn’t seem to work very well, and so you have to kind of take the Hot Jupiters seriously.

Before I go on, let me mention that, by now, Hot Jupiters are not the only kind of planets that have been seen this way. There are also planets in–now known to have much longer orbits, up to a few years. These are harder to see for two reasons. First of all, it takes you a few years to see them. And second of all, when the orbits get longer, the velocities that they induce go down, because things in long orbits go slowly. But, nevertheless, now we’ve been able to see a bunch of things.

Oddly, in many cases, they turn out to have highly elliptical orbits, in some cases. Not the Hot Jupiters, not the ones that are close in. Those all are more or less circular. But some of these longer ones have highly elliptical orbits. That’s also very weird in terms of our theories of planetary formation because one of the things that our theories were designed to explain was the fact that all the major planets in our own Solar System have orbits that are close to circular. It does a very good job of explaining that and then, naturally enough, has trouble explaining the ones we see that are in highly elliptical orbits–highly elliptical–yes, I didn’t–highly elliptical orbits, in some cases. And just so you know, the way you recognize a highly elliptical orbit is it’s not sinusoidal anymore. It’s got some other shape. So, these come in: periodic but non-sinusoidal velocity curves.

So, all this is very amusing and you pile up all these very strange kinds of planets, or what you think are planets. But there’s still sort of the nagging question of whether these radial velocity curves might be explainable in some other way. And it would be awfully nice to have evidence of some other kind for the existence of these planets.

This is, you know, what happens in science. You find some kind of fairly strong evidence for something, but it would be way stronger if you found two different kinds of evidence. Different–collected in different ways or reflecting different aspects of what you’re observing that both point in the same direction.

And, at a certain point along the way, about six years ago or so, a new kind of evidence for the existence of these planets was discovered. And the first such case, which is now a very famous star for this reason, was something called HD209458; that’s the name of the star. And this was a Hot Jupiter system. So, this is the name of the star; Hot Jupiter was discovered in the usual way by Doppler measurements, by radial velocity measurements.

And then, something else was discovered. So, let me show what they found in this system. All right, so let me explain what’s plotted here. This is the brightness of this system, not the radial velocity this time–the brightness against time. And so, here it is on the 9th of September, 1999. And somebody is measuring the brightness of this thing. And it’s set up in units so that the average brightness is 1. And you can see, these measurements have a little bit of error in them. They scatter around. And then, at a certain point there’s a dip in the brightness of the star for a few hours; notice this is in days. This is a tenth of a day, so 2.4 hours, something like that. So, for a few hours the brightness of this thing dips down to about 98% of its–of the brightness it has, so 2–it loses 2% of its brightness for a little while and then it comes back up.

And then, interestingly enough, seven nights later on the night of the 16th of September, it did the same thing. Now, seven nights is an important number for this particular system, because it turns out that the orbital period of its Hot Jupiter, which was already known at the time, is three and a half days. So, this is exactly two orbits later. The exact same dip occurred. You couldn’t see it one orbit later because three and a half days later it’s daytime, and one of the features of astronomy is that you do it at night. And so you have to wait two day–two orbits to see the same thing again.

So, every orbit–there appears to be this little dip. And what is happening is that this is a system that’s almost exactly edge-on. And what’s happening is that the planet is passing in front of the star, and once per orbit the planet gets in the way of the star. The planet’s this little thing, the star’s a big thing. And a small amount of the star’s light is obscured by the planet. This is called a transit. So, let me just write that down. And then, transits are discovered–yeah, okay, we’ll come back to the overheads in a minute because I want to show you more plots. And it’s the planet getting in the way of the starlight. And what this tells you, also, is how big the planet is, because you’ve got a little disc in front of a big disc. And the amount of light that’s obscured–this 2%–tells you what the ratio of the area projected by the planet, compared to the area projected by the entire star, is.

So, this gives you an additional piece of information. You already know the mass of the thing because you’ve measured the radial velocity. Now, we also know its size. So, this was very interesting. And it is, as I was saying just a second ago, an entirely different kind of confirmation of the existence of this planet. So, there’s no pulsation going on here, because some–you not only are getting the changes in velocity of the planet you’re seeing–of the star, you’re also seeing the light of the star diminish when the planet passes in front of it.

Chapter 2. Discovery of Planetary Transits [00:07:38]

And then, so, they decided this was interesting, and so they did this same experiment, except with this Hubble Space Telescope instead of with some ground-based telescope. This is what you see with Hubble, and you can see why Hubble is a better telescope than the ground-based stuff. This is exactly the same plot. This is the average brightness of the system outside of the transit, so this is 1.000. This is .985 so it’s dropped down 1.5% in brightness. This is in days and in–this is a tenth of a day here, each of these big ticks is .05 of a day. And here is the star going along perfectly normally. And you get better measurements because you’re not distorted by the atmosphere. And then, all of a sudden, the thing drops and it gets–has this very particular shape to the light curve, to the curve of brightness with time.

This shape is perfectly explained by the hypothesis that you’re passing an opaque disc across the surface of the star. As the disc touches the star it starts to–and gradually more and more of the disc is over the star. You get this steep drop here. And then, this rounded part down on the bottom comes about because when you look at a star, the center of the star, the central portion of the star looks a little bit brighter than the edges because, if you think about looking at a sphere, if you look at the center, you’re looking right at it. If you’re looking at the side, you’re sort of grazing the edge and it turns out there is something called “limb darkening,” which comes about because of this. So, stars, if you look at the Sun for example, the edges of the Sun look a little fainter than the middle. And so, what happens is, as this disc passes across the face of the star, it obscures successively brighter parts of the star until you get down to here. Then, it obscures gradually fainter parts of the star until it gets to the edge. Now, the disc is–as it goes up here, is passing beyond the edge of the star.

So, this is exactly the shape of a light curve you would predict if you passed an opaque disc in front of a star. And it really works out remarkably well. In fact, there’s a line underneath these points, you can see it off here and off here, which is a prediction. And you can’t see the line because it’s under the point so nicely. So, this works out incredibly well. This is almost for sure an opaque disc, namely the planet, passing in front of the star.

So, transits are discovered–the dip in light due to planet passing across the star. Now, this does not happen in every Hot Jupiter, because you have to be lined up pretty, pretty perfectly in order for the planet to pass in front of the star. That is to say if–here’s you, here’s an observer, here’s the star. And, if the planet–if the orbital plane of the planet looks like this, then when the planet’s in front of the star, it’ll be below it. So, if you think about it, imagine a planet that’s orbiting like this. Here’s its star. And it never passes in front of the star, because when it’s in front of the star, it’s below the star. Whereas, if it–if it’s exactly edge-on, then once per orbit, it will pass in front of the star. But, you have to have a very precise alignment for that to take place–so, requires a precisely edge-on alignment. But, if you have such an alignment, you know how these dips ought to line up with the radial velocity curve.

So, now what you see is, you measure the brightness of the star versus time, and you see these dips. Here’s a dip. Then one orbit later, you get another dip, and so forth. If you then, at the same time, measure the radial velocity–and again, this is the radial velocity of the star–then you know how this has to take place. Because here you are. You’re looking at it. And the moment where the dip takes place, the planet’s got to be exactly in front of the star. That means the planet is at this point in its orbit, going that way, for example, and the star is in this part of its orbit, going that way–which means this–the radial velocity at the moment the dip occurs has to be zero. Because for them to be lined up, one in front of the other, they’ve both got to be going sideways. And shortly before that, the star was moving away from you, because they’re moving into position, like this. Shortly afterwards, the star is coming towards you. And, remember that positive radial velocities are coming toward–or going away from you, negative velocities are coming towards you. So it used to be–it used to be going away from you, positive. It’s now at zero at the point of the dip. And then it’s going to be coming towards you, so it has to be that these dips take place at that point in the curve. And so, here again, it’s got to be like this. And so, the way this has to work out is something like this. So, you can predict what the radial velocity has to be at the particular moment where the transit occurs.

And so this works. This works for HD–what is it? 209458. So this works out. So, now you’ve got a lot of evidence that this really is a planet. Not only is it moving the star back and forth the way you expect a planet to do, it’s also passing in front of that star at exactly the moment you expect it to pass in front of the star, and the shape of the dip that it creates is exactly what you would expect if you pass an opaque disc in front of a star. So now, you’ve got a whole bunch of different kinds of evidence. You can ask, “Does this prove it’s a planet?”

And then you get into this problem with scientific proof. What does it mean to prove something in science? You could probably figure out some clever way that it’s actually a pulsating star, which has a star spot on it that somehow precisely mimics exactly the way a planet would behave. Impossible that this would–well not–I should be careful with that word. Highly improbably that this would actually occur in real life, so I think, you know–people have the feeling that science is truth, somehow, and that, you know, that you can prove things in science, kind of, to a mathematical certainty.

That actually isn’t the case. The legal standard, you know, which you’re familiar from cop shows, of beyond a reasonable doubt, applies in science as well. And that’s actually a more appropriate standard to use for anything, which, in the law or in the natural world, in which you try and reason by induction. And so I would say that this, plus this, plus the shape of the–of the spectral lines, which we talked about last time, plus the shape of these dips–that’s proof way beyond a reasonable doubt that there’s a planet around this particular star. And that really ended the conversation. Yes?

Student: Is it always directly edge-on or could there be a case in which it’s [inaudible]

Professor Charles Bailyn: Right.

Student: –sort of like a little bit below or a little bit [inaudible]

Professor Charles Bailyn: So, is it always edge-on? Well, orbits don’t change, so for this object it’s always edge-on. For most objects, it is not edge-on, and so, in fact, what had happened was, by the time they discovered this one, there were a couple of dozen of Hot Jupiters known. None of the rest of them do this, because in all the rest of them, the orbit isn’t aligned properly, and so the planet never goes in front of the star. And so, in the vast majority of cases, you don’t get this. And so, they only discovered this after they’d found so many of them, that one of them turned out to be aligned properly, you know, just by chance.

Student: Is there–it possible for an orbit to not–never pass in front of the center of the star?

Professor Charles Bailyn: No. What it does is it passes–it’s got to do this, it’s got to have some moment where the planet is as far towards you as it can be, and then it turns around and comes back. But for most orbits, at that point, the planet will either be below or above the star from your line of sight. So, imagine this orbit as the planet goes–here’s a star. Planet’s going around the star. It reaches its furthest forward point, but it’s well below the star from your line of sight. So, it depends on the angle of the orbital plane. Does that make sense?

Student: It, it doesn’t have to pass through the center of the star, it could pass [inaudible]

Professor Charles Bailyn: Oh, oh –

Student: [inaudible.]

Professor Charles Bailyn: Yes, sorry, exactly right. It doesn’t have to pass through the center of the star. It can graze the tip at the bottom of the star a little bit. And in fact, in this object, you can tell how close to the center it goes by the exact shape of the curvature down at the bottom of that light curve. Because, you know what the expected distribution of brightness across the face of the star is. You also know something about the radius of the star. This is supposed to be a solar-type star, presumably has a radius of the Sun. If it passes across, sort of grazes the bottom, then the dip will be shorter, because it will pass through faster. And so, you can figure out exactly what the trajectory across the thing is. Most of the time it misses. And in this case, you can figure out that the angle of the inclination, so-called, which is 90 degrees if it’s exactly edge-on, is 80–I think 88 point something, I don’t remember the answer. Because, it doesn’t go exactly across the center, it goes, sort of, sort of halfway down.

So yeah, that actually gives you additional information. How long the dip is and what the exact shape of the thing, tells you which part of the star it passes across. Yes good, thanks Bethany. Other questions about this? Yeah?

Student: Have we ever discovered a planet through transit without having discovered it previously?

Professor Charles Bailyn: Right, have we discovered a planet through transit without having discovered the previous radial velocity curves? Yes, and we’ll get to that. Because, let me just say this: as soon as this was discovered, people got way excited, because it’s quite difficult to make these kinds of precise radial velocity measurements. You have to have very specialized equipment. Only a few people in the world can do it. There’s this bunch of people in California who can do it. There’s this bunch of people in Switzerland who can do it.

Us ‒ normal astronomers, don’t have that kind of expertise and equipment, but measuring a change in brightness of a star by 2%, that’s easy. I can do it up on Science Hill [an area of the Yale campus where the Astronomy Department is located] in our little observatory up there. In fact, I have done it for this star. You can–if the timing were better, this star is up in the summertime, unfortunately. If it were up in the fall we would have this be an exercise in Astro 155 [a Yale Astronomy class], because it’s entirely straightforward to go and measure a 2% difference in brightness in a star. Anybody, you know, with 2,000 bucks’ worth of equipment, you can go out into your backyard and do this experiment. This is a big deal.

Chapter 3. Limits of Finding Planets Directly from Transits [00:19:53]

So, as soon as that was possible, everybody got fired up, you know, “I’m going to play this game myself.” And we all laid very elaborate plans for going out and finding zillions of planets. And the problem is that it has to be exactly aligned edge-on for this to even occur. And so, most stars with planets–this doesn’t happen. And so, you would have to observe many, many, many stars in order to see this one time. So you have to–while it’s easy to do for any one particular object, it’s hard to discover them this way because you have to do it in bulk. You have to look at many stars at once.

So then, people thought, well, great, we know how to do this. We’ll look at many stars at once. We’ll take pictures of star clusters, of–where there are lots and lots of stars. And we’ll just keep taking pictures of these star clusters over and over again. You’ll look at 30,000 stars at a time, and if one of them has a dip, we’ll find that dip. And so, the way we’ll deal with the fact that this doesn’t always occur is by looking at star clusters. And so, they tried this, again, with the space telescope, because it works better at doing this kind of thing.

The problem with star clusters is that the stars are really close to each other, so from the ground it just looks like a mush. In this case, you have to see the stars separately. So, they took a particular star cluster–also the advantage of doing it from space is no daytime, and so, you can observe continuously. So, they took eight consecutive days of Hubble Space Telescope time and did nothing but look at a star cluster, a cluster called–famous cluster called 47 Tuc, 37 stars. They took repeated images of this star cluster, and they figured, we ought to see some number of planets by the transit method, first, in this cluster.

So just, here’s what the cluster looks like. So this, on the left, is a ground-based picture of this cluster, and you can see what the problem with observing this stuff from the ground is. If you look down in the middle, it’s all mushed together. You wouldn’t be able to pick out individual stars. But then, this box here, blown up to the right-hand side of the picture–this is what that little box looks like from the Hubble Space Telescope. And now, you have the resolution to observe each of these stars, or many of them individually. And so they took eight nights of Hubble Space Telescope time–that’s a lot of time on the space telescope. The space telescope costs about a $1,000,000 a day to run. And so, this is 8,000,000 bucks’ worth of observing time.

Okay, so what did they expect to see? So, finding planets directly from transits. And so, they observe a cluster of stars–30,000 stars at a time. So, what do you expect? Well, it turns out, from the radial velocity studies, they had gone and looked at a lot of, sort of, Sun-like stars. So, 30,000 more or less Sun-like stars, I should specify, from the radial velocity measurements from the Doppler measurements. They got answers like approximately 1 out of 10 stars–this is a rough estimate ‒ have Hot Jupiters. And then, how precisely aligned do they have to be? Approximately 1 out of 100 Hot Jupiters is aligned properly to get a transit.

And so, now, you have a prediction. You look at 30,000 stars. A tenth of them have planets, that’s 3,000 planets. One hundredth of those will be aligned up in such a way that you can see a transit. That’s thirty transits. Predict– thirty transits. And it was that kind of calculation–this is just a rough estimate, but they had done this much more precisely. It was that kind of estimate that persuaded the people at the Space Telescope Institute to allocate all these many hours of space telescope time to this project.

The result was zero transits, none. Not seen. And this was a little distressing, except it didn’t take people very long to figure out that they should have known this in advance. And this is–you know, you get a result and then of course people–you get an unexpected result, and then people start writing papers which say, well, of course that’s what you should have gotten. Any fool could have predicted that you would not see any transits in a star cluster, except none of the fools did.

Let’s see, so–but, in retrospect, it was clear that this wasn’t going to give you the thing you thought because of two factors. First, in–why? So, first factor: in clusters, the stars are really close together. Stars–they sometimes collide or more often have near collisions. And when a star comes cruising into your planetary system, the star has a lot of gravity. It’s going to completely wreck the orbits of the planets because you’re going to have the gravity of a second star. And it turns out that what this does is it liberates the planets. And so, it will disrupt planetary orbits. So, you kind of don’t expect there to be any planet; you expect there to be planets in the cluster, but they’ll be free floating planets sort of wandering around the cluster, because they will have been detached from their parent star by incoming stars–by close encounters with other stars in the cluster.

Put it this way. The nearest star to the Sun, beside the Sun, Alpha Cen, is about a parsec away. In a cubic parsec, at the center of one of these clusters, there are a million stars. And so, there are a million stars packed into the space where only one star exists in our corner of the galaxy. So, they run around–you know, if you were in a cluster, if you were in a planet on a cluster, and you were looking up at the sky, the constellations would change from year to year, because the stars are so nearby that their motions would be readily apparent. And once every few hundred million years, a star would come cruising into your Solar System and detach all of the planets from the star. And so, you don’t expect there to be any planets.

You also don’t expect there to be any planets for an entirely different reason, which is, one of the things that had been discovered as they were piling up all these Hot Jupiters found by the Doppler Shift method, is that stars are more likely to have planets–have planets–if they have high amounts of heavy elements–heavy elements. Now, let me explain that. Most stars–stars are mostly hydrogen and helium. Astronomers do chemistry in a very peculiar way. We have–we consider there are three kinds of things in the universe. There’s hydrogen, there’s helium, and there’s metal. Chemists–everything else is a metal. If don’t care if it’s oxygen, carbon, whatever. The chemists get really uncomfortable with this. But, you know, it’s like the supposed primitive tribes. I’m not sure these–this actually exists, but the linguists say there are tribes in the world where they count one, two and many. Well, this is how astrono–I don’t know if such tribes exist except for the astronomers, who really do. And we count, one, two, and many. And we call any chemical element heavier than helium a metal.

Chapter 4. Metallicity and Planetary Migration [00:28:54]

So, we have this concept called metallicity, which is defined to be the fraction of something of elements heavier than hydrogen and helium, which are the first two in the Periodic Table, as you probably know. So, everything else is a metal. The metallicity of the Sun–Sun’s metallicity–is about 2%. And the metallicity of the Solar System is therefore about 2%, because the Sun’s got all the mass. And, high metallicity stars, by which I mean, metallicities greater than the Sun–greater than solar–are more likely to have planets.

This makes perfect sense. This is the first thing in a little while that’s made any sense–because, how do you make a planet? Well, planets aren’t made out of hydrogen and helium. Planets are made out of the other stuff. We’re made out of silicon and iron, and the–Jupiter’s got a lot of ice, and so all these kinds of heavy elements–you don’t make–you can’t make a planet if all you’ve got is hydrogen and helium because there’s nothing solid to have it form. And the only way you get to keep your hydrogen and helium, the 98% of the stuff that’s hydrogen and helium, is if you already have a big core of heavier–either rocks, or ice, or something else–if you already have some metallic, in the astronomical sense, core. And so this makes perfect sense. If you don’t have any metals, you can’t be forming planets.

And star clusters of the kind that Hubble observe are known, and this particular one is, to consist of low metallicity stars. In the case of 47 Tuc, the one we looked at, it’s–the metallicity of the thing is, I think, about a fifth that of the Sun. So, it’s got very substantially fewer heavy elements. So, no planets.

So, in two different ways this was a mistake, right? But that was only realized afterwards. And, it’s unfortunate that it was a mistake in two different ways. Because if it was a mistake in only one different way you would have learned something from this, because you would have confirmed the idea that a star–close stellar encounters strip planets off of stars–except maybe it’s only because of the low metallicity. Or, you would have confirmed the idea that low metallicity stars can’t have planets; except in this case, maybe it’s just because of the stars and the planets have been stripped away. So it’s kind of unfortunate that there were two excellent explanations different from each other about why you should have predicted this result before you obtained it.

However, having done that, it was clear what the next experiment had to be: that you wanted to go out and try and measure these transits in some region that’s a little less dense, and a whole lot more metal rich. So, next experiment, which was done last summer, didn’t look at a star cluster. It looked at the center–a region close to the center of the galaxy. So, this is lots of stars, but significantly less dense than what you would get in the center of a cluster.

Fortunately, they had put up a bigger camera into the space telescope since then, so you could cover more of the sky, which was useful. This is the camera; by the way, you may have read, over the weekend, that Hubble’s had a little bit of a problem. The electronics in this wide field camera have shorted out. And so, Hubble’s kind of in trouble for–until they get the next visit, because its major camera is now blind. And this happened, I should say, 12 hours after the deadline for submitting proposals. So, there had been almost 1,000 proposals submitted from around the world, of which, maybe only a fifth would ever get done. People in our department and basically every department in the whole–astronomy department in the whole world were going nuts trying to prepare their detailed proposals for using the thing. They submitted them, and a few hours later it broke. And so, then there was this nice little email from the people at the Space Telescope Institute saying, “uhh, you might want to reconsider, and we’ve created a new deadline three weeks from now so that you can revise and extend.”

There are other instruments that still work but the cameras aren’t as good. And so, now, everybody’s scratching their head and thinking, can I actually do this, and if I can, what’s the good strategy? Do I want to try and do it now when the competition’s going to be much less because the instruments are lousy? Or, do I want to wait until after September 2008, when they’re scheduled to go up replace the camera and repair the thing, and try and do it with the good instruments then, when everybody else in the world is going to want to do their experiment? And so, we’re all grappling with this at the moment.

However, last summer this was working like crazy. And they did another one of these ten consecutive days of observations, but this time of the center of the galaxy, which has lots of stars–but less dense than in the center of the cluster, and also has the advantage that many of these stars, most of them, are high metallicity stars. So, hopefully, this will work, right? Because you’ve eliminated both of the excellent reasons why it didn’t work the last time.

So, here is the field of view that they were looking at. This is a tiny piece of the center of the galaxy. Lots and lots and lots of stars, which is good, because you want to see them. And these little circles here, which are numbered from 1 to 16, I believe, are circles around little Sun-like stars. You can see the stars in the middle of those circles; you probably have a hard time seeing. Let’s turn the lights down. This is kind of a nice picture. This is what the center of the galaxy looks like to the Hubble Space Telescope. And these bright things–the colors are sort of quasi-real. These things are red giant stars and solar type stars. The center of the galaxy is quite far away–are really quite faint, you can barely see it. See in the middle of this circle there’s a little star there, that’s a Sun-like star in the middle of the galaxy. And these circles are these stars in which they found–in which they found transits. So, in this case, it worked. So, it’s true that one or the other or both of those reasons they had why it didn’t work in the star cluster, were in fact the reason it didn’t work in the star clusters. Because here’s a situation where those problems don’t exist. And now they found sixteen of these things, which is pretty close to the amount you would have expected.

And so now it is–these are planets, which have been discovered first by the transit method. I should say, there are a couple of others that have been discovered. First by the transit method, from people at the ground just going out and looking at random stars. And in some of those cases, they have been done the opposite thing, and gone back and found the radial velocity measurements after having discovered the tran–the planet by transits. You can’t do radial velocity on these guys because they’re too faint, and it’s just not going to work out.

Okay, how’re we doing? All right. Now, a couple of consequences of this. If you have both radial velocity measurements, which tell you the mass of the planet, and transits, which tell you the radius of the planet, then you know something very important. You know the density. Density–then, you get the density.

Density is usually written down with the Greek letter ρ, for some reason, which I don’t understand, but it’s always done that way, so we’ll do it too. And density is defined as mass of something divided by its volume. And so, for a spherical object, the volume–if you go back to some geometry book, you can look this up. 43 π times the radius cubed, and that’s the density.

The density, if you–the density of water is about–is 1 gram per cubic centimeter. Now, of course, that’s a lousy set of units. We do things in kilograms per cubic meter. That’s, as it turns out, 1,000 kilograms per cubic meter. So, if you picture a cubic meter, that’s a pretty huge aquarium. It’s actually pretty heavy. And, let’s see, is this right? 102, 106 times a gram–yeah, that’s right. And, in fact, interestingly enough, this is the definition of a gram. This is where they came up with that metric unit–is to make it work out so that the density of water is one–is exactly 1 gram per cubic centimeter. You have to specify the temperature, too, because–but, so, that’s a typical density of water, which is on ice, right?

Rocks have higher density–much higher density. That’s why a handful of iron is heavier than an equivalent sized handful of snow, or something like that. So, if you know the density, you can tell something about the composition of the planet. And it turns out that the Hot Jupiters, in the few cases we now have–it’s not just one case, it’s several cases–Hot Jupiters have low density. They really are ice balls. They’re not made out of rock. And so, an idea you might have had about where the Hot Jupiters come from is, well, in these high metallicity stars, there’s just a whole bunch more rock, and the Earth-like planets kind of get big. But that isn’t what happened. These things really are made out of ice. And now you have a problem, because you know how far away they are from the star. And the temperature of these things–the surface temperature of these things is, like, 1,000 degrees. This is not a good place to put a snowball, all right? You put a snowball in some place which is 1,000 degrees–we won’t specify the place–and something bad is going to happen to it.

Now, the–and so, therefore, how could these planets have formed? And so the idea–the current thinking on this is an idea called migration. And the idea behind migration is that you make Jupiters in the Outer Solar System, where they belong. And then, through some mechanism, which people have ideas about, but which aren’t–isn’t at the moment really specified–these things, after they are formed, they migrate into the Inner Solar System. And the reason this is a useful thing to do is that a big thing melts slowly. The reason for that is that the surface area to volume ratio is low. Volume goes up as the cube of the radius–surface area, goes up–as the square. If you shine a light on something, the amount of energy it picks up depends on how big it is, not on how massive it is. And so, changes of temperature in interacting with your environment are less, the bigger you are. This is why, by the way, arctic animals tend to be big: because they’re trying to survive in an environment that’s much colder than they are. And so, they generate energy by their volume and they lose it out their skin, by their surface area. So, you want to have a lot of volume compared to your surface area. Big things melt slowly. So, you can’t have ice planetesimals in the Inner Solar System. But you can have something the size of Jupiter. And it’ll melt, but it’ll take longer than the age of the Solar System, or even the age of the universe, to do so.

So this is the idea. And of course, the key point here is this migration. And there are ideas about why this should happen, but it isn’t wholly clear.

Chapter 5. Consequences and Limits of the Idea of Planetary Migration [00:43:32]

Now, one thing, a consequence of this idea, is that there are no terrestrial planets. No terrestrial planets, because as this Jupiter is moving inward, if there’s an Earth in the way, it’s going to either knock it out of its orbit completely, or the Earth will run into Jupiter and become incorporated into that planet. So, if you’ve got a Jupiter-size system in–near where your Earth-like planet is orbiting, that Earth-like planet’s in big trouble for exactly the same reason the planets are in trouble, in general, when another star comes through, because you’ve got something much more massive coming by, screwing up your orbit. So, there are no terrestrial planets. Their orbits are disrupted by the migrating Jupiter.

Now, in fact, I have to qualify this a little. There was a paper that showed up in the literature, a few months back, with some clever way of preserving the terrestrial planets as the Jupiter came by. I have to say, I don’t fully appreciate the force of this argument. It is perhaps true–because I haven’t read the paper carefully enough, but I feel obliged to mention that somebody, at least, has an idea about how you can avoid it. But, in sort of straightforward terms, you don’t expect there to be terrestrial planets in a situation where a Jupiter has migrated from the Outer Solar System to the Inner Solar System. Questions? How are we doing? Yes?

Student: I was just wondering what caused the Hot Jupiters to migrate?

Professor Charles Bailyn: What causes the Hot Jupiters to migrate? This is a subject of some discussion among the experts. The idea is that when the Jupiter forms, remember it forms out of a disc of gas? There might still be a substantial residual gas and dust disc. And as the Jupiter plows through it, the friction with that disc slows it down. And if you slow down the orbit of a planet, it’ll gradually fall inwards. That’s one idea.

There are some–there are other ideas. But it isn’t clear. And if it were clear, you would have predicted it to happen. And indeed, there’s a whole problem with the migration theory. So, problem with migration is, sometimes it doesn’t work. Because, Jupiter in our Solar System is where Jupiter is. It didn’t migrate. It has to work–needs–so, the problem with the migration system is, it needs to work, but not always. It also can’t work too well, because if it works too well, then the Jupiter falls right into the Sun, right? So, it has to work most of the time, but not all the time, but not too well. This is a complicated balancing act. And, whatever theory you propose, whether it’s this friction with a dust disc, or anything else, you’ve got a little problem with this whole concept. Because you have to tune this mechanism up so that it takes most Jupiters, moves them into the Inner Solar System, and then stops working at just the right point to leave you with a whole bunch of Hot Jupiters, most but not all of the time.

All right, that’s as much as we know about it. That’s–you know, you got to come back three years from now and see if we’ve straightened this out, because that’s where we are at the moment. All right, more later.

[end of transcript]

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